[Mathkoll] ESI Senior Research Fellow Programm / Prof. van Nieuwenhuizen

Institut für Mathematik sekr.mathematik@univie.ac.at
Tue Jan 6 10:53:48 CET 2004


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Liebe KollegInnen,

auf die im Rahmen des ESI Senior Research Fellow Programms 2003/2004
Fortsetzung des Kurses
"Anomalies in D=10 N=1 and N=2B supergravity from quantum mechanical path
integrals"
von Prof. Peter Van Nieuwenhuizen (C.N. Yang Institute for Theoretical
Physics, Stony Brook)
weise ich hin.
Ich bitte auch Ihre StudentInnen zu informieren.

Eine ausfuehrliche Ankuendigung findet sich in den Attachements und unter
www.esi.ac.at/activities/courses.html


Mit herzlichen Gruessen

Joachim Schwermer
als Koordinator des Programms

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\documentclass[12pt]{article}
\pagestyle{empty}
\begin{document}
\begin{center}
{\sc
Part II of the ESI Course on\\
N=3D1 and N=3D2 Supersymmetry and Supergravity\\
by\\
Erwin Schr\"odinger Senior Fellow}\\[5pt]
{\large\bf
Prof. PETER VAN NIEUWENHUIZEN}\\=20
(C. N. Yang Institute for Theoretical Physics, Stony Brook)\\
\end{center}
\smallskip
\begin{center}
\large\bf
Anomalies in D=3D10 N=3D1 and N=3D2B supergravity
from quantum mechanical path integrals
\end{center}
\smallskip
{\bf Content:}
We compute the one-loop gravitational anomalies in quantum field
theories with spin $1\over2$, spin $3\over2$, and selfdual
antisymmetric tensor gauge fields in the loop, and external
gravity and Yang-Mills gauge fields (the antisymmetric tensors
are represented
by bispinors). The anomaly is given by $An=3D\lim_{\beta\to0}{\rm Tr}\,
J \exp -\beta R$, where $J$ is the Jacobian for a gravitational
symmetry transformation, and $R$ is a particular regulator.

We replace the operators in this expression by quantum mechanical
operators. We pass from the operator formulation to the corresponding
path integral by rewriting all operators in Weyl-ordered from,
applying a lemma by Berezin. As complete sets of states for the fermions
we use coherent states, and equal-time contractions and Feynman rules
are unambiguously derived by not taking the continuum limit too soon.

Then we compute the gravitational anomalies in any (even) dimension.
We apply those formulas to $D=3D10$. For $N=3D2B$ supergravity the
anomalies cancel by themselves, but for $N=3D1$ supergravity the
anomalies are cancelled by a counter term which we derive from
descent equations, and this is only possible if the gauge group
is SO(32) or $\mathrm E_8 \times \mathrm E_8$.

\bigskip

\begin{center}
{\bf Dates:\\
1.) Thursday, January 8, 2004, 16:00--18:00\\
2.) Tuesday, January 13, 2004, 16:00--18:00\\
3.) Tuesday, January 20, 2004, 16:00--18:00\\
4.) Tuesday, January 27, 2004, 16:00--18:00\\[18pt]
Location: Institute for Theoretical Physics, TU Vienna,\\ Wiedner =
Hauptstr. 8-10,
seminar room, 10th floor}\\
(take the elevator located in the yellow part of the building!)
\end{center}
\end{document}
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